Michael D. Cohen, President Trump’s longtime personal fixer, will soon be parting from the lawyers who are representing him in a potentially damaging and wide-ranging federal investigation into his business dealings, according to two people familiar with the case.

Mr. Cohen has not yet been approached by the prosecutors conducting the inquiry to seek his cooperation, according to two people briefed on the case. But as the investigation into him continues, and with his legal team in flux, the pressure on Mr. Cohen to cooperate may well intensify.

Mr. Cohen’s current lawyers — a three-man team from the firm of McDermott Will & Emery — are expected to stay with him for the rest of the week as they struggle to complete a laborious review of a trove of documents and data files seized from their client in a series of extraordinary early-morning raids two months ago. But after that review is finished, Mr. Cohen will seek new legal counsel, the people familiar with his case said. They added that the issues concern the payment of legal bills to his lawyers and their relative lack of experience with the federal prosecutors’ office in New York that is leading the investigation.

Mr. Cohen has been facing scrutiny for months, but the explosive case burst into public view on April 9 when federal agents armed with search warrants descended on his office, apartment and hotel room, hauling away eight boxes of paperwork, about 30 cellphones, iPads and computers — even the contents of one of his shredders. The materials were seized on the orders of prosecutors in Manhattan who have been trying to determine whether Mr. Cohen broke the law in any of his business projects, including hush-money payments he made to two women who claim they had affairs with Mr. Trump.

The Cohen inquiry is separate from the one being run in Washington by the special counsel, Robert S. Mueller III, who is looking into potential ties between Mr. Trump, his associates and Russia. But ever since the raids involving Mr. Cohen took place, Mr. Trump’s lawyers have confronted the specter that the New York-based investigation could persuade Mr. Cohen, who has a wife and two children and faces the prospect of devastating legal fees, to cut a deal and share his intimate knowledge of Mr. Trump with Mr. Mueller’s team. Mr. Cohen, after all, worked for Mr. Trump for years as a lawyer and self-described “fix-it guy,” guarding his boss’s secrets and helping him to navigate some of the most sensitive episodes in his personal and professional life.

Among those episodes was one involving the pornographic film star, Stephanie Clifford, who is better known as Stormy Daniels. Mr. Cohen has admitted paying Ms. Clifford $130,000 in the run-up to the 2016 election to keep her mouth shut about an affair she claims she had with Mr. Trump. Though Mr. Trump initially denied any knowledge of the payment — which came at a moment when he was under stiff criticism for his relationships with women — in a striking reversal, he later admitted he had known about it.

It is not uncommon for clients — even those, like Mr. Cohen, who have not yet been charged with a crime — to change their lawyers in the middle of a case. And while Mr. Cohen’s split from the McDermott team, which was first reported by ABC News, marked a significant turn in the proceeding, there was no certainty that he would strike a deal with the prosecutors and thus place Mr. Trump into further legal jeopardy.

One person with knowledge of the legal staffing change said that Mr. Trump’s camp was “very displeased” with the way the Cohen investigation had so far been conducted. Mr. Trump himself has told people he is angry at Mr. Cohen over the messiness of the situation — especially those aspects involving Ms. Clifford. But the president has also indicated to allies that he is worried that if he pushes Mr. Cohen away too hard, it could increase the likelihood that Mr. Cohen will offer information to the government.

From the start, the McDermott team of lawyers — led by Stephen M. Ryan — was an awkward fit in a case that began in Washington with a referral by Mr. Mueller, but soon moved to New York. Mr. Ryan, based in Washington, is not as familiar with the Manhattan federal prosecutors’ office as many local lawyers are and some in Mr. Cohen’s orbit suggested that he needed a lawyer with more experience in the New York courts.

One person familiar with Mr. Cohen said that there also may have been discomfort within the McDermott firm itself about Mr. Ryan staying on the case given the high-profile — and often sordid — nature of some of the allegations that have surfaced. This person said in the past few weeks there have been discussions with a number of prominent defense lawyers in New York about representing Mr. Cohen going forward.

For the next few days, however, Mr. Ryan and his team will continue working on their review of the vast trove of materials seized from Mr. Cohen, a process meant to determine which among the nearly four million files taken are protected by the attorney-client privilege that Mr. Trump enjoys in his dealings with Mr. Cohen. That review is crucial because it will ultimately shape the contours of the evidence that the prosecutors will be able to use in their investigation.

As recently as two weeks ago, Mr. Cohen’s lawyers told the judge in the case, Kimba M. Wood, that they were working around the clock to finish the review.

“We are moving heaven and earth,” the lawyer, Todd Harrison, told Judge Wood. “We have people working all night. We have people sleeping on couches in our offices. We have people who worked all through the Memorial Day weekend.”